Question: The sum of two angles is $71^\circ$. Angle 2 is $49^\circ$ smaller than $2$ times angle 1. What are the measures of the two angles in degrees?
Explanation: Let $x$ equal the measure of angle 1 and $y$ equal the measure of angle 2. The system of equations is then: ${x+y = 71}$ ${y = 2x-49}$ Since we already have solved for $y$ in terms of $x$ , we can use substitution to solve for $x$ and $y$ Substitute ${2x-49}$ for $y$ in the first equation. ${x + }{(2x-49)}{= 71}$ Simplify and solve for $x$ $ x+2x - 49 = 71 $ $ 3x-49 = 71 $ $ 3x = 120 $ $ x = \dfrac{120}{3} $ ${x = 40}$ Now that you know ${x = 40}$ , plug it back into $ {y = 2x-49}$ to find $y$ ${y = 2}{(40)}{ - 49}$ $y = 80 - 49$ ${y = 31}$ You can also plug ${x = 40}$ into $ {x+y = 71}$ and get the same answer for $y$ ${(40)}{ + y = 71}$ ${y = 31}$ The measure of angle 1 is $40^\circ$ and the measure of angle 2 is $31^\circ$.